Recently a relationship was discovered between the number of permutati
ons of n letters that have no increasing subsequence of length > k, on
the one hand, and the number of Young tableaux of n cells whose first
row is of length less than or equal to k, on the other. The proof see
med quite unmotivated and artificial. Here we describe the sequence of
events that led to the discovery, via computer algebra, of this relat
ionship. (C) 1995 Academic Press Limited